Mike Dunleavy told Mark Begich he had a question that he figured "people really want to know."

"Are you in negotiations with the Walker camp to cut a deal for one of you to drop out before the election?" Dunleavy, the Republican candidate for governor, asked into the microphone at a governor's candidate debate Thursday in downtown Anchorage, in front of a lunchtime crowd at the Hotel Captain Cook.

The question about Begich, the Democratic candidate, and incumbent Gov. Bill Walker, an independent, came two days after the bombshell announcement that Lt. Gov. Byron Mallott was stepping down from office and the campaign after making unspecified "inappropriate comments" to a woman.

Begich fired back to Dunleavy: "Mike, first off, as we're here, we're having conversations with you, and I'd like you to drop out," sparking laughter from the audience.

With Mallott's sudden resignation and Election Day less than three weeks away, people are wondering: Will there be changes to the Walker or Begich campaigns? Are last-minute attacks loaded for launch in the final days of the campaign? What exactly happened with Mallott?

Continuing in his response to Dunleavy during the debate, Begich said: "There's always opportunities to have conversations about what's best for Alaska."

Mike Dunleavy, right, listens to comments from Gov. Bill Walker and Mark Begich in the Debate on Resource Development at the Hotel Captain Cook on October 18, 2018. (Marc Lester / ADN)

Begich's campaign manager, Nora Morse, responded "yes" in a text message after the debate when asked if Begich will be in the governor's race on Nov. 6, Election Day. Walker said after the debate it was his intention to stay in the race as well.

During the exchange between Begich and Dunleavy, Walker raised his hand to have a say in the matter. The crowd laughed. The moderator, John Sturgeon, allowed it.

"Well, I gotta tell you, the Republican Party contacted me some time ago, asked me to be their candidate, it was after you filed," Walker said. "There's all sorts of conversations going on out there."

Alaska Republican Party chairman Tuckerman Babcock was quick to dispute what Walker said. He sent out an emailed statement less than an hour after the debate ended. The email's subject line: "Governor Walker Needs a Nap and an Iced Tea to Relax."

Babcock said Walker's chief of staff Scott Kendall had reached out to Republican Party leaders, who responded that Walker could run as a Republican if he wanted to.

"We predicted the reception would NOT be warm," Babcock's statement said. He added that "all of those inquiries from the governor occurred prior to the State Convention of the Alaska Republican Party held in Anchorage last March."

Kendall said Thursday evening that Babcock mischaracterized what happened. Sometime in late 2016 or early 2017, Kendall said, Babcock proposed to him the idea that Walker change his registration to Republican and run in the Republican primary.

"I am a thousand percent sure he initiated the idea," Kendall said. "He not only had this offer, he had quite detailed plans about it."

He added: "We can take polygraphs at the same time, anytime."

Kendall took that information to the governor, who ultimately turned it down, he said.

Walker, surrounded by reporters after the debate, clarified that the Republican Party didn't talk to him directly, but to "a senior person in our organization." Walker said he "rejected that proposal." He's independent, he said, and he's happy to keep it that way.

The debate Thursday was also noteworthy for the question that wasn't asked, but has consumed Alaska politics this week: What did Mallott say, and to whom, that prompted him to resign?

Thursday's event — hosted by a several natural resource development groups — was the first with the three candidates since Mallott resigned. Mallott's name wasn't mentioned during the one-hour debate.

Walker has previously described Mallott's comments as "inappropriate overtures" and said Thursday he would not go into any further detail.

"I'm going to honor my commitment to the victim and make sure she's not just somehow drawn into this sort of thing," Walker told reporters after the debate. He stood next to his wife, First Lady Donna Walker.

When addressing the Alaska Federation of Natives convention in Anchorage earlier Thursday, Walker called Mallott his brother, closest friend and soulmate.

"That will not change," he said at AFN. "Sometimes leaders fall down and it's what we do after the fall that defines who we really are."

Walker said Mallott did the right thing by owning up to his mistake and resigning.

He reiterated that to reporters after the afternoon debate. So did Donna Walker. She also spoke out against speculations circulating about what Mallott may have said that triggered his resignation.

"There are outlandish things that are being speculated about what happened, who the victim was and they are so far from anything that's true," she said.

She did not say what Mallott said or to whom.

Early voting in the Nov. 6 election starts Monday. The Alaska Division of Elections has also already sent out more than 20,000 ballots.

The Alaska Oil and Gas Association, the Alaska Support Industry Alliance, and several other groups hosted Thursday's debate. Aside from the back-and-forth, candidates answered a list of questions about resource development issues, including their positions on the Stand for Salmon ballot initiative, whether they would commit state resources to support an Arctic National Wildlife Refuge lease sale in court if environmental groups litigate, and the state's hatchery program.